We will deduce the flow equation in the UV regime. In this regime, all the sums can be replaced by integration following the arguments of [1]}, essentially because the divergences of the integral approximations are the same as the exact sums. The method consists to a formal expansion of the r.h.s of the Wetterich equation (REF ) in power of couplings, and identification of the corresponding terms in the l.h.s. The r.h.s involves in general some contractions between the \(F_{k(n)}\)  and the effective propagator \(\partial _kR_k\) . And in this UV regime, only the melonic graphs contribute.
